DIFFERENTIAL EQUATIONS

SEMESTER-I, PAPER-I

CBCS/ SEMESTER SYSTEM

B.A./B.Sc. MATHEMATICS (w.e.f. 2020-21 Admitted Batch)

DIFFERENTIAL EQUATIONS

SYLLABUS (75 Hours)

Course Outcomes:

After successful completion of this course, the student will be able to;

1. Solve linear differential equations
2. Convert non exact homogeneous equations to exact differential equations by using integrating
3. Know the methods of finding solutions of differential equations of the first order but not of the first
4. Solve higher-order linear differential equations, both homogeneous and non homogeneous, with constant
5. Understand the concept and apply appropriate methods for solving differential

Course Syllabus:

UNIT – I (12 Hours)

Differential Equations of first order and first degree:

Linear Differential Equations; Differential equations reducible to linear form; Exact differential equations; Integrating factors.

UNIT – II (12 Hours)

Orthogonal Trajectories:(Cartesian and polar forms)

Differential Equations of first order but not of the first degree:

Equations solvable for p, Clairaut’s Equation.

UNIT – III (12 Hours)

Higher order linear differential equations-I:

Solution of homogeneous linear differential equations of order n with constant coefficients; Solution of the non-homogeneous linear differential equations with constant coefficients by means of polynomial operators. General Solution of f(D)y=0.

General Solution of

f (D) y = Q

when Q is function of x ,

1/f (D) is expressed as partial fractions.

P.I. of f(D)y = Q when Q= be^ax

P.I. of f(D)y = Q when Q is bsinax or b cos ax.

UNIT – IV (12 Hours)

Higher order linear differential equations-II:

Solution of the non-homogeneous linear differential equations with constant coefficients.

P.I. of f(D)y = Q when Q= bx^k

P.I. of f(D)y = Q when Q= e^axV , where V is a function of x.

P.I. of f(D)y = Q when Q= xV , where V is a function of x.

P.I. of f(D)y = Q when Q= x^mV , where V is a function of x.

UNIT –V (12 Hours)

Higher order linear differential equations-III :

Method of variation of parameters(with out non constant coefficients), The Cauchy-Euler Equation, Legendre’s linear equations.

Co-Curricular Activities(15 Hours)

Seminar/ Quiz/ Assignments/ Applications of Differential Equations to Real life Problem

/Problem Solving.

Text Book :

Differential Equations and Their Applications by Zafar Ahsan, published by Prentice-Hall of India Pvt.     Ltd, New Delhi-Second edition.

Reference Books :

1. A text book of Mathematics for B.A/B.Sc, Vol 1, by N. Krishna Murthy & others, published by S.Chand & Company, New
2. Ordinary and Partial Differential Equations by Dr. M.D,Raisinghania, published by Chand & Company, New Delhi.
3. Differential Equations with applications and programs – S. Balachandra Rao & HR Anuradha- Universities
4. Differential Equations -Srinivas Vangala & Madhu Rajesh, published by Spectrum University